Universities should be allowed to decide what they charge students under a radical shakeup of higher education which would see the existing cap on tuition fees lifted.

A new system of financing universities will allow for a 10% increase in student places to meet rising demand for a degree-level education, the Browne review proposes.

Lord Browne, the former chief executive of BP, said universities that charged the highest fees would have to demonstrate they are widening access to students from poorer homes.

"There are a variety of things they can do in that area, including offering scholarships for living expenses," he told the Guardian.

Graduates will start repaying the cost of their degrees when they start earning £21,000 a year, up from £15,000 under the current system, the review recommends.

The independent review recommends that the current cap on fees of £3,290 a year be removed.

Institutions charging more than £6,000 will have to pay a rising percentage of each additional £1,000 as a levy to government. So a university that charges £7,000 will receive 94% of this fee, while one that charges £10,000 will receive 81%. At £6,000, the university receives the full fee.

Lord Browne said today that he did not expect students to be deterred by debt.

"There is a lot of evidence that students don't just look at debt, but at the prize at the end as well, which is significant earning potential. If you look at the 40% of students who study part-time, we don't offer them anything, but they still come and study part-time."

The Browne review says that should change and part-time students should have equal entitlement to government support for tuition fees.

"Part-time study provides a second chance for people who missed out earlier in their lives, and it is important to level the playing field between part-time and full-time study," the review says.

The coalition government is not bound to adopt Lord Browne's proposals. Lifting the cap on fees could provoke a rift with the Lib Dems, who are pledged to oppose any increase in fees.

Careers advice is in need of "a radical overhaul", according to the Browne review.

"Part of empowering our young people is ensuring they have the right information, advice and guidance to make the correct choice. This means careers advice in all schools of the kind currently being given in the private sector."

Lord Browne said students would dictate which universities flourished and which did not.

"The word is out - students talk to each other. I want to encourage that. This is about the student experience, and if people are pulling a fast one, it will come out very quickly."

The review calls for "student charters" that give information about employment rates and course quality. It also proposes raising the amount poorer students receive to cover their living expenses while at university.

"A lot of people won't pay back anything like what the government has given them. The bottom 20% [of earners] would pay back less than they do today." Only the top 40% of earners would pay back the full cost, the review says.

It recommends there should be "no single fixed price" for fees. Different courses cost different amounts, Browne said. Institutions will have to persuade students that the charges they put on their courses represent value for money. "Institutions are all different and they provide a wide range of different courses. We want this diversity to flourish," the review says.

Arts and humanities degrees could become more expensive and potentially less popular under Browne's proposals. The review says the government could remove public funding from all but "priority" subjects, such as medicine, science and engineering.

It says there needs to be a "closer fit between what is taught and the skills needed in the economy".

Under Browne's plans, popular universities would be able to expand, while others may be forced to contract.

Browne calls for extra support for students from families with an income below £60,000. The government should write off any debt that graduates have not managed to pay after 30 years, the review says. Currently, debt is cancelled after 25 years.

The review says: "Our higher education system is world-renowned, but too often it enshrines the power of universities and not the power of students. These reforms will put students in the driving seat of a revolutionary new system.

"Under these plans universities can start to vary what they charge but it will be up to students whether they choose the university. The money will follow the student, who will follow the quality. The student is no longer taken for granted; the student is in charge.

"We have been guided by three principles: participation, quality and sustainability. Any student who has the academic potential should be able to participate in and benefit from higher education.

"Students do not pay anything upfront. Only graduates pay … according to the level of their earnings. Under our proposals, the bottom 20% of earners will pay less than today and only the top 40% of earners will pay back close to the full amount."

The National Union of Students said Browne was handing a "blank cheque" to universities.

Aaron Porter, NUS president, said: "If adopted, Lord Browne's review would hand universities a blank cheque and force the next generation to pick up the tab for devastating cuts to higher education. The only thing students and their families would stand to gain from higher fees would be higher debts.

"A market in course prices between universities would increasingly put pressure on students to make decisions based on cost rather than academic ability or ambition. Those already feeling the pinch will clearly be unwilling to take such a gamble and face being priced out of the universities that would opt to charge sky-high fees.

"There is no clear assurance that a hike in fees would improve student choice or quality and the evidence since fees tripled four years ago shows that neither student satisfaction nor quality has improved." Nearly 30 Lib Dem backbenchers are prepared to rebel by voting against the government over a rise in tuition fees, the National Union of Students claimed yesterday.

At the time of the election, all sitting Lib Dem MPs, including Nick Clegg and Vince Cable, signed up to a pledge to vote against any increase in fees. The coalition agreement allows the Lib Dems to abstain.

The review calls for the merger of a super quango for higher education. The Higher Education Funding Council for England, which distributes funding on behalf of the government, would be combined with the sector's watchdog for fair access, its quality regulator and its complaints watchdog.

The review took more than 150 submissions and heard from 36 witnesses.